No cross-interactions among different tensor fields with the mixed symmetry (3,1) intermediated by a vector field

TL;DR

This paper proves that under certain physical assumptions, different tensor fields with mixed symmetry do not interact with each other through a vector or p-form gauge field, except for a single coupling per tensor field.

Contribution

It establishes the non-existence of cross-interactions among multiple tensor fields with mixed symmetry mediated by a vector or p-form gauge field under specified conditions.

Findings

Only one tensor field couples to the vector or p-form gauge field.

No interactions occur among different tensor fields with mixed symmetry.

Results align with the uniqueness of the graviton in General Relativity.

Abstract

Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a collection of free massless tensor gauge fields with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field, respectively a $p$-form gauge field, are addressed. The main result is that a single mixed symmetry tensor field from the collection gets coupled to the vector field/$p$-form. Our final result resembles to the well known fact from General Relativity according to which there is one graviton in a given world.